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T-Totals. I am going to investigate T-totals in relation to the T-number on different sized grids. I am then going to investigate the relationship between the T-total of a T-shape in 1 area of a grid to when it is translated, using any vector, to another

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Introduction

For this Piece of coursework I am going to investigate T-totals in relation to the T-number on different sized grids. I am then going to investigate the relationship between the T-total of a T-shape in 1 area of a grid to when it is translated, using any vector, to another area of the grid. 7 8 9 13 18 A T-shape consists of five numbers, when added together theses numbers create the T-total. The T-number is the number at the bottom of the T-shape. E.G. - The T-total for this shape would be 7+8+9+13+18 = 55 - The T-number for this shape would be 18 Throughout this Coursework I will refer to the T-total as 'T' and the T-number as 'N'. I started by investigating the relationships on a 5x5 grid, making sure I worked in a systematic way in order to make it easier to compare the results and discover a comparison. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 T-number (n) T-Total (T) 12 25 13 30 14 35 I can see from the table that as N increases by 1, T increases by 5, using this information I can begin to create a formula. ...read more.

Middle

I then worked out the formula for a 8x8 grid using the same process. T-number (n) T-Total (T) 18 34 19 39 20 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 I can see from the table that, like on the other grid, as N increases by 1, T increases by 5. So I know that the beginning of the formula is the same. 18(n) x 5 = 90 90 - 34(T) = 56 So, T = 5n - 56 Proof I created the T-shape, for this grid, below in order to prove my formula. N-17 N-16 N-15 N-8 N So, T = n-13+n-12+n-11+n-6+n T = 5n - 42 Therefore, according to this T-shape my formula is correct. I then worked out the formula for a 9x9 grid using the same process. T-number (n) T-Total (T) 20 37 21 42 22 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ...read more.

Conclusion

I will use a 10x10 grid and experiment with different vectors to see if there is a pattern. H amount moved horizontally V amount moved vertically N-2G+1 N-2G N-2G-1 N-G N N-2G+1 +h N-2G+h N-2G-1+h N-G+h N+h Original T-shape T-shape moved right H So,T-total = n-2g+1+h+n-2g+h+n-2g-1+h+n-g+h+n+h = 5N - 7G + 5H N-2G+1 N-2G N-2G-1 N-G N N-2G+1 -Gv N-2G-Gv N-2G-1-Gv N-G-Gv N-Gv Original T-shape T-shape moved up V So,T-total = n-2g+1-gv+n-2g-gv+n-2g-1-gv+n-n-g-gv+n-gv = 5N - 7G + 5GV These can be proven by checking it within the grid below. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 34 44 45 46 47 48 49 50 51 52 35 54 55 56 57 58 59 60 61 62 36 64 65 66 67 68 69 70 71 72 37 74 75 76 77 78 79 80 81 82 38 84 85 86 87 88 89 90 91 92 39 94 95 96 97 98 99 100 N-2G+1 +1 N-2G+1 N-2G-1+1 N-G+1 N+1 N-2G+1 -10 N-2G-10 N-2G-1-10 N-G-10 N-10 T-shape moved right 1 T-shape moved up 1 In conclusion I have found that the T-total of a vector H is V T = 5N - 7G + 5H - GV ...read more.

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